Measuring based on a capacitive sensor has proved to have a simple principle and to provide a reliable method in the measuring of physical quantities, like for instance acceleration, pressure or angular velocity. The capacitive measuring is based on a change in the gap between two surfaces of a pair of electrodes of the sensor. The capacitance between the surfaces, i.e. the capacity for storing electric charge, depends on the area of the surfaces and on the distance between the surfaces. Capacitive measuring can be used already at rather low measuring ranges of acceleration, pressure or angular velocity.
The basis for the structure of small capacitive sensors is a thin-film structure manufactured on silicon. The thin membrane forming one of the electrodes bends under influence of the quantity to be measured and thus changes the capacitance to be measured.
Frequently it is desirable that the output of the sensors is linearly dependent on the quantity to be measured.
The capacitance of a planar capacitor is determined by the equation:
      C    =                  ɛ        0            ⁢              A        d              ,in which A is the area of the electrodes and d is the distance between them. Thus, the capacitance has an inverted linear proportionality to the distance d. The transfer function of a sensor, which, in addition to the planar capacitor, possesses a parallel stray capacitance C00, in the case of a capacitive pressure sensor, for example, is determined as follows:
      p    =                  p        0            ⁡              (                  1          -                                    C              0                                      C              -                              C                00                                                    )              ,where C is the measured capacitance, and p0, C0 and C00 are constants by sensor. A sensor solution according to the transfer function like this can be cost-effectively implemented also by means of conventional and inexpensive analog electronics.
Further, for an acceleration sensor solution, for example, which consists of two coupled planar capacitors to be measured, this function of Δx can be formulated
                    V        out            ⁡              (                  Δ          ⁢                                          ⁢          x                )              =                                        C            1                    -                      C            2                                                C            1                    +                      C            2                              =                                                                  ɛ                0                            ⁢                              A                                  d                  -                                      Δ                    ⁢                                                                                  ⁢                    x                                                                        -                                          ɛ                0                            ⁢                              A                                  d                  +                                      Δ                    ⁢                                                                                  ⁢                    x                                                                                                                          ɛ                0                            ⁢                              A                                  d                  -                                      Δ                    ⁢                                                                                  ⁢                    x                                                                        +                                          ɛ                0                            ⁢                              A                                  d                  +                                      Δ                    ⁢                                                                                  ⁢                    x                                                                                      =                              Δ            ⁢                                                  ⁢            x                    d                      ,which, thus, is a linear function.
During the measuring event, in practice, the sensor's movable electrode, made of a thin foil, is being bent in a curved shape due to the quantity to be measured, for example. In the case of an acceleration sensor, the displacement of the seismic mass can be non-planar and, in addition to a pure translational motion, it can be partly or fully rotational. Thus, linearity error will be introduced in using the transfer functions mentioned the above, since the moving capacitor gap will not stay planar.
According to prior art, there are several solutions aiming at compensating for non-linearity introduced in capacitive sensors during the measuring process. In one solution the sensor's moving electrode, such as the foil in a pressure sensor, can be provided with a stiffener, whereby, at the location of the metal electrode, the foil moves as a plane, and the transfer function mentioned above can be used. Such a solution according to prior art is disclosed in, for example, U.S. Pat. No. 4,609,966.
One solution, according to prior art, for reducing non-linearity is making the sensor's moving electrode, such as, for example, the foil of a pressure sensor, non-uniform. This can, for example, be implemented in a known manner by adding support structures, such that the foil locally achieves maximal deflection at more than one point. By means of this solution, the capacitance dynamics of the measuring is achieved with less deflection, and, consequently, reduced non-linearity. Such a solution according to prior art is disclosed in, for example, U.S. Pat. No. 5,801,313 and U.S. Pat. No. 6,352,874.
Compensation of non-linearity introduced in capacitive sensors in the measuring process can also, according to prior art, be attempted by using a more complicated transfer function. This requires separate compensating electronics. Also, there is a disadvantage in that calibration will have to be performed at a larger number of points, should the model contain more independent parameters.
One solution for reducing non-linearity is using a touch-mode sensor according to prior art. Thereby, for a pressure sensor, for example, the pressure response will already be linear at its operational range and it will have a high sensitivity. Such a solution according to prior art is disclosed in, for example, US Application 2002/0092356 and JP Application 2002/195903. Disadvantages of the sensor of the touch-mode type are hysteretic behavior and poor tolerance for excessive pressure.